Pullback dynamics of 3D Navier–Stokes equations with nonlinear viscosity. (August 2019) - Yang, Xin-Guang; Feng, Baowei; Wang, Shubin; Lu, Yongjin; Ma, To Fu
Abstract: This paper is concerned with pullback dynamics of 3D Navier–Stokes equations with variable viscosity and subject to time-dependent external forces. Our main result establishes the existence of finite-dimensional pullback attractors in a general setting involving tempered universes. We also present a sufficient condition on the viscosity coefficients that guarantees the attractors are nontrivial. We end the paper by showing the upper semi-continuity of pullback attractors as the non-autonomous perturbation vanishes.